I'm looking for a Wiki software, knowledge base tool or something similar with the following features:
* reading access for users without account can be configured
* collaborative real-time editor for the content
* basic wiki features like categories, markup or WYSIWYG, search bar etc.
Open source is preferred but not a must. Especially the real time editor gives me headaches. The only software i know which has all these features is Confluence, but as i said i would prefer free software. Confluence also has tons of features which are useless for my usecase. Any other ideas?

Taskade lets you edit notes, tasks, and documents in real-time, collaboratively, across web, desktop, and mobile. It's free to use for teams. It is simple and flexible, documents in Taskade can be displayed and edited in various views, from task list to kanban to mindmap view.

I'd take a look at GitBook.
It might cover most of your needs:
- Made for documentation
- Open source
- Collaborative (desktop and web editor)
- You're able to create categories (and use them as navigation)
- Searchbar, markup...
Here is an example: https://frontendmasters.com/book...

That's pretty much the use case we created Corilla to solve. We were technical writers and developers at Red Hat struggling with this same problem, and built a collaborative editor for our distributed colleagues, adding in version control, a unique "collections" mode, and even private and publish documentation hosting. All bundled to help you just get back to writing.
We have plans to open source but are in the process of releasing a new kbase first. Always willing to help out Product Hunt family in the meantime.